Every rational number has a base-2 representation, but only the ones with denominators that are powers of 2 will require a finite number of bits to fully represent it.

For example,

$\dfrac12 = 1\cdot2^{-1} = 0.1_2$

$\dfrac14 = 1\cdot2^{-2} = 0.01_2$

$\dfrac34 = \dfrac12 + \dfrac14 = 0.11_2$

$\dfrac{1023}{1024} = 1 - \dfrac1{2^{10}} = 1_2 - 0.0000000001_2 = 0.1111111111_2$

whereas a number whose denominator contains anything else like 1/3 will need an infinite number of bits to represent it exactly.

$\dfrac13 = \dfrac1{2^2} + \dfrac1{12} = \dfrac1{2^2} + \dfrac1{2^4} + \dfrac1{48} = \dfrac1{2^2} + \dfrac1{2^4} + \dfrac1{2^8} + \dfrac1{192}$

and so on, so that it has a repeating but non-terminating base-2 representation

$\dfrac13 = 0.010101\ldots_2$

5 0

1 year ago

(ii) The probability the tiles are both the same colour is 16 45 Show that x2 - 6x + 5 = 0.<br>

nika2105 [10]

Answer:

i think probably x = 1 or 5

Step-by-step explanation:

x²-6x+5 =0

so (x-1)(x-5) = 0

so x = 1 or 5

6 0

1 year ago

Use a proportion to determine the number of children age 5 in a kindergarten class if 80% of a class of 20 children are that age

igor_vitrenko [27]

Answer:

16 children

Step-by-step explanation:

80% of 20 children comes out to 16 children who are of age 5.

If desired, rewrite "80%" as "0.80" and use that 0.80 as the multiplier of 20:

0.80(20 children) = 16 children.

4 0

3 years ago

The standard form of 6050000 is given by​

The standard form of 6050000 is given by